Quoting Ghostcrawler (source – from blue.mmo-champion.com cuz I’m not going to dig through 25 pages of paladin QQ to find the original GC update):
I made some clarifications to my initial post.
You can use Hand of Protection during the internal cooldown, just not on yourself. The idea is to prevent the paladin from being able to [...]

Ghostcrawler has provided a list of the upcoming paladin changes, due out with the next content patch (source):
We have already announced or suggested all of these changes would be forthcoming in the next minor content patch. I thought I would list them all in one place for ease of use.
Divine Shield: Penalty changed so that [...]